2026/07/17 by Giovanni Bruccola
#math.OC
We address the problem of optimally placing a limited number of sensors to reconstruct high-dimensional signals without knowledge of the underlying dynamics. The task is formulated as a nonconvex combinatorial optimisation problem and recast as a weakly convex constrained projection problem. This reformulation allows us to compute ε-global solutions using the Inexact Cutting Sphere algorithm. We further propose the Inverse Cutting Sphere algorithm, which starts from any feasible heuristic solution and either improves it by a prescribed tolerance ε or certifies its ε-global optimality. The framework is evaluated on pressure reconstruction for NACA airfoils using XFOIL data.